Memory is very important to G5 and it is a must to have Mac compatible low density memory mounted in matched pairs, and not cheaper, high density PC memory. If that is what you are using sounds like a faulty logic board. If you have the original system discs, try and boot from disc one and run Apple Hardware Test.

Hang on to those original install discs like grim death! Using OS X.7 or later make a bootable USB thumb drive before running Installer!